Download Resistivity Measurements Using the Model 2450 SourceMeter SMU

Number 3247
Application Note
Se­ries
Resistivity Measurements Using the
®
Model 2450 SourceMeter SMU Instrument
and a Four-Point Collinear Probe
Introduction
Electrical resistivity is a basic material property that quantifies
a material’s opposition to current flow; it is the reciprocal
of conductivity. The resistivity of a material depends upon
several factors, including the material doping, processing, and
environmental factors such as temperature and humidity. The
resistivity of the material can affect the characteristics of a device
of which it’s made, such as the series resistance, threshold
voltage, capacitance, and other parameters.
Determining the resistivity of a material is common in both
research and fabrication environments. There are many methods
for determining the resistivity of a material, but the technique
may vary depending upon the type of material, magnitude of
the resistance, shape, and thickness of the material. One of the
most common ways of measuring the resistivity of some thin, flat
materials, such as semiconductors or conductive coatings, uses
a four-point collinear probe. The four-point probe technique
involves bringing four equally spaced probes in contact with a
material of unknown resistance. A DC current is forced between
the outer two probes, and a voltmeter measures the voltage
difference between the inner two probes. The resistivity is
calculated from geometric factors, the source current, and the
voltage measurement. The instrumentation used for this test
includes a DC current source, a sensitive voltmeter, and a fourpoint collinear probe.
To simplify measurements, a single instrument, the Model
2450 SourceMeter® Source Measure Unit (SMU) Instrument,
can be used. This instrument can source and measure both
current and voltage and can be configured to display resistance
or resistivity. The Model 2450 enables the user to choose a test
current over many decades (from picoamps to amps), as well
as measure voltage with resolution in the microvolt range. The
Model 2450 is pictured in Figure 1 connected to a Signatone
four-point collinear probe. This configuration is set up to
measure the resistivity of a semiconductor wafer.
This application note explains how to perform resistivity
measurements on materials using the Model 2450 and a fourpoint collinear probe.
The Four-Point Collinear Probe Method
The four-point collinear probe technique involves bringing four
equally spaced probes in contact with a material of unknown
resistance. The probes, mounted into a probe head, are gently
placed in the center of the wafer as shown in the resistivity test
circuit in Figure 2.
HI
HI
LO
V
Source current
from 1 to 4
Measure voltage
between 2 and 3
LO
4-Point
Collinear Probe
1
2
3
4
Semiconductor Wafer
Figure 2. Four-point probe resistivity test circuit.
The two outer probes, 1 and 4, are used for sourcing current.
The two inner probes, 2 and 3, are used for measuring the
resulting voltage drop across the surface of the sample.
The volume or bulk resistivity (ρ) is calculated as follows:
π V
V
r = ____ ___ t k = 4.532 ___ t k
ln2I
I
Figure 1. Model 2450 SourceMeter SMU Instrument with the Lucas/Signatone
Corporation (Gilroy, CA) Model SP4 4-Point Probe Head and S-302 Test Stand
measuring the resistivity of a sample.
where:
ρ = the volume resistivity (Ω-cm)
V = the voltage measured between probes 2 and 3 (voltage)
I = the magnitude of the source current (amps)
t = the sample thickness (cm)
k =a correction factor based on the ratio of the probe to
wafer diameter and on the ratio of wafer thickness to
probe separation
For some materials such as thin films and coatings, the sheet
resistance, or surface resistivity, is determined instead, which
does not take the thickness into account. The sheet resistance (σ)
is calculated as follows:
π V
V
σ =____ ___ k = 4.532___ k
ln2I
I
where:
σ = the sheet resistance (Ω/square or just Ω)
Note that the units for sheet resistance are expressed in
terms of Ω/square in order to distinguish this number from the
measured resistance (V/I).
Using the Kelvin Technique to Eliminate
Lead and Contact Resistance
Using four probes eliminates measurement errors due to the
probe resistance, the spreading resistance under each probe,
and the contact resistance between each metal probe and the
semiconductor material. Figure 3 is another representation of
the four-point collinear probe setup that shows some of the
circuit resistances.
Source Current
HI
HI
R L1
LO
LO
V
R L2
R L3
R L4
R L = Lead Resistance
R C = Contact Resistance
R S = Sample Resistance
V = Measured Voltage Between
Probes 2 And 3
Only the voltage drop due to R S2 is
measured by the voltmeter.
1
3
2
RC
RC
1
2
R S1
V
R S2
4
RC
RC
3
4
Using Compensation Techniques to
Correct for Voltage Offsets
For increased accuracy, a technique to compensate for voltage
offsets can be applied. There are two common methods of
compensation to reduce voltage offsets: the offset compensation
method and the current reversal method.
One method takes a voltage measurement at zero amps and
then subtracts this value from a reading taken at the desired
test current. This method is called offset compensation and is
an option that can be performed automatically in the resistance
mode of the Model 2450.
The other technique, the current reversal method, is similar
to the other method but offers better signal to noise ratio. This
technique cancels voltage offsets by making two measurements
with currents of opposite polarity. When the two measurements
are averaged, the voltage offsets are mathematically eliminated
from the final result. This technique can be performed using
software to control the Model 2450 or by downloading a script.
More information on either of these two methods can be
found in Keithley’s Low Level Measurement Handbook, available
at www.keithley.com.
Making Connections to the Four-Point Probe
The four-point probe can be connected to the Model 2450
using either the front panel banana jacks or the rear panel
triax connectors. A circuit diagram showing the Model 2450
connected to the four-point probe is shown in Figure 4. The
Force terminals are connected to probes 1 and 4, and the Sense
terminals are connected to probes 2 and 3. The rear panel triax
terminals should be used for higher impedance materials. In
this case, all cables, the probes, and the sample should also be
electrostatically shielded. Some materials are photo sensitive
and would require that the material be light shielded during the
measurement.
Model 2450 SourceMeter
R S3
HI
LO
Figure 3. Test setup showing circuit resistances.
Force LO
Sense LO
Sense HI
Notice that the current flows through all the resistances in
the first and fourth set of leads and probes, as well as through
the semiconductor material. However, the voltage is only
measured between probes 2 and 3. Given that between probes
2 and 3, the current only flows through RS2, only the voltage
drop due to RS2 will be measured by the voltmeter. All the
other unwanted lead (R L) and contact (RC) resistances will not
be measured.
V
Force HI
The R L terms represent the test lead resistance. RC represents
the contact resistance between the metal probe and the
semiconductor material. The contact resistance can be several
hundred to a thousand times higher than the resistance of the
sample material, which is represented by RS.
4-Point
Collinear Probe
1
2
3
4
Semiconductor Wafer
Figure 4. Connecting the Model 2450 to a four-point collinear probe head.
Configuring the Test
After the probe is connected to the input terminals of the Model
2450 and the sample is placed on the mounting chuck, follow
these steps to measure the resistivity of a sample:
1.On the Model 2450, press the FUNCTION key and select
Source Current and Measure Resistance (or Voltage).
Choose the desired source current and voltage source limit
(compliance) by using the front panel touch buttons. Set the
Sense Mode to 4-Wire by pressing the MENU key, Measuring
Settings, and then Sense Mode button.
2.Lower the probe head so the pins are in contact with
the sample.
3.Turn on the output of the Model 2450 and observe the
reading. If the readings appear unstable, try increasing the
test current. Make sure that the voltage drops between Force
HI and Sense HI and also between Force LO and Sense LO
do not exceed 5V.
4.Calculate the resistivity from the readings.
The resistivity can be automatically calculated using either the
built-in “mx+b” Math Function or by using a script. A script is a
list of commands that can be downloaded into the Model 2450.
The results of executing a simple script to calculate the resistivity
in ohms/square from the measured resistance are shown in
Figure 5. Notice the calculated resistivity is displayed in the
bottom half of the touchscreen.
technique using a user-prompted test current to measure
the resistance. Then, the surface resistivity in ohms/square is
calculated and displayed on the bottom half of the front panel.
The results of executing the script are shown in Figure 5.
Steps to Generate, Download, and Execute a Script
Here are the simple steps to create and execute a script on the
Model 2450:
1.By using either Notepad or Test Script Builder (TSB)
Software, create a script to perform a resistivity measurement
using the TSP command set. TSB is a software tool included
with the Model 2450 that will enable you to execute
the script before you download it to the unit. For your
convenience, you can copy the script listed in this application
note and modify it.
2.Save the script as a .tsp file on a USB drive, and insert the
USB drive into the Model 2450 front panel USB port.
3.Once the USB drive is inserted, all .tsp files on it will appear
in the MANAGE SCRIPTS window. This can be accessed by
pressing the MENU key and then Manage Scripts as shown in
Figure 6. Press on the desired USB script and press the “<”
key to add it to the Internal Scripts list.
Figure 5. Model 2450 displaying the measured resistance and resistivity
of a sample.
Creating and Downloading Scripts to the Model 2450
To correct for voltage offsets by performing current reversals or
to display the measurements with units of Ω/square or Ω-cm,
you can easily create and download a script to the Model 2450. A
script is a collection of TSP commands that you can download to
the instrument using a USB drive. The scripts are executed from
the front panel and are stored in non-volatile memory. These can
be added or deleted from a front panel menu.
An example script to perform resistivity measurements
is listed in Appendix A. In this script, the Model 2450 is
programmed to perform a current reversal compensation
Figure 6. The Manage Scripts window enables the user to download
scripts from a USB drive and store them into non-volatile memory.
(continued on next page)
4.Once the script is stored into internal memory, the user can
execute the script from the Home Page as shown in Figure 7.
At the top of the Home Page, press the “No Script” button to
view the available scripts. Press the desired script and the test
will automatically execute.
Figure 7. Pressing the desired script will automatically execute that script.
Conclusion
The Model 2450 SourceMeter SMU Instrument is an ideal tool for
measuring resistivity on samples using the four-point collinear
probe method. This SMU instrument can source current and
measure voltage or resistance using a four-wire method to
prevent the lead and contact resistance from affecting the
measurement. The Model 2450 enables the user to specify the
test current, measure the resistance using offset compensation,
calculate the resistivity, and shows the results on the display of
the instrument.
Appendix A
--Script for Measuring Resistivity of a Material Using a 4-Point Probe
--Function to calculate resistivity
function resistivity(R1, R2)
return 4.5324*((math.abs(R1)+math.abs(R2))/2)
end
--Reset the instrument
reset()
--Set to source current
smu.source.func = smu.FUNC_DC_CURRENT
--User input test current
testcurrent = display.input.number("Enter a Test Current", display.NFORMAT_PREFIX, 0, 0, 1)
--Negative value of user test current
smu.source.level = -1*testcurrent
--Measure voltage
smu.measure.func = smu.FUNC_DC_VOLTAGE
--Set to 4 wire measure mode
smu.measure.sense = smu.SENSE_4WIRE
--Set the measurement unit to Ohms
smu.measure.unit = smu.UNIT_OHM
--Turn on the output
smu.source.output = smu.ON
--Take a resistance measurement
res1 = smu.measure.read()
smu.source.level = testcurrent
res2 = smu.measure.read()
--Calculate the resistivity from the reading
local res = resistivity(res1, res2)
--Set the display to the user swipe screen and display resistivity
display.changescreen(display.SCREEN_USER_SWIPE)
display.settext(display.TEXT1, string.format("Resistivity"))
display.settext(display.TEXT2, string.format(" = %.3e Ohms/Square", res))
--Turn the output off
smu.source.output = smu.OFF
Specifications are subject to change without notice. All Keithley trademarks and trade names are the property of Keithley Instruments, Inc.
All other trademarks and trade names are the property of their respective companies.
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© Copyright 2013 Keithley Instruments, Inc.
Printed in the U.S.A
No. 3247
3.13.14